Yes, they do. iPhones don't seem to do that, but old GSM phones did it (like my first phone, Ericsson T20, which got released in 2000). Androids have read reports in the default message app, if I'm not mistaken.
No, they don't. The protocol supports delivery report only. And the meaning of that report isn't necessarily what you believe or wish it to be:
...the exact meaning of confirmations varies from reaching the network, to being queued for sending, to being sent, to receiving a confirmation of receipt from the target device...(https://en.wikipedia.org/wiki/SMS)
Nor does it test the recipient understanding of the content. But that's missing the point.
The app lets you know that your message delivered to the recipient and then lets you know that it was opened (not merely viewed as a notification). This is a useful feature that SMS lacks.
The point was that being displayed on my screen doesn't mean I read it. For instance, I have a problem where sometimes I'll log in to my phone and an app will be active. I don't want that app; I need to do a bank transaction. But now someone thinks their message has been read, when so far from reading it I don't even know it exists! It was just displayed on my screen for half a moment when my eyes and my attention was somewhere else. (Another common problem I have is when I send a message, and then they reply so fast that the message arrives at about the same time as I'm trying to return to the homescreen to ensure I get a notification when the message arrives. Well unfortunately the message arrived first, got marked as read and no notification exists. After twenty minutes I realise what happens but maybe I've already offended someone by "reading" their message and ignoring it.)
Delivered vs read is only accurate if you have an eye tracker.
* SMS don't have read receipt.
* SMS depends on cellular connectivity.
* SMS and MMS have very limited media transfer support.
* SMS don't have feature similar to groups.